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 5 unknown digits (Posted on 2014-05-13)
Each of the three consecutive 3-digit numbers n, n+1, n+2 divides N=146,8XX,XXX, where each X represents a digit below 6 .

 See The Solution Submitted by Ady TZIDON No Rating

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 Python solution | Comment 2 of 5 |
(In reply to Solution by Jer)

for n in range(100,1000):
k = n * (n+1) * (n+2) / 2
if k > 146855555:
break
if 146800000/k != 146855555/k:
NN = (146855555/k) * k
chk = 0
for i in list(str(NN))[4:]:
if i > '5':
chk = 1
break
if chk == 0:
print n, NN

produces the same two results that Jer found, and one other:

`100 146803500  123 146800500  195 146822130  `
`Edit: But that last one isn't valid - as Jer noted, `
`dividing by 2 is valid if n is even.  `
`146822130 is not divisible by 196, so strike that `
`off the list.   `

Edited on May 13, 2014, 3:04 pm

Edited on May 13, 2014, 3:05 pm
 Posted by tomarken on 2014-05-13 15:01:18

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